Mr Shorten’s win put Ms Bryce, Australia’s first female Governor-General, in a potentially difficult position because she has the power to dismiss the prime minister.

However, Mr Abbott rejected Ms Bryce’s offer to resign, saying her service had been “exemplary” and she should stay on until her term ends in March next year.

“The Governor-General offered to leave office early to avoid any perception of bias but due to the fact that she will retire in March next year and that the government commands the House of Representatives with a significant margin, I have thanked her for her magnanimity but declined to accept her resignation,” Mr Abbott said.

‘‘Her excellency ... has served the people of Australia with distinction and has provided a gracious note to our constitutional arrangements through her widespread engagement with the community I believe it is only fit and proper that she be permitted to conclude her term.” The unusual dilemma arose because Mr Shorten is married to Ms Bryce’s daughter, Chloe. Ms Bryce has previously sought legal advice on whether the marriage posed a conflict of interest, but Australia’s solicitor-general advised it did not.

Mr Shorten became Labor leader after the party — the oldest in Australia — held a primary vote of party members for the first time in its history.

The new voting system was introduced by Kevin Rudd, the former prime minister, who later stepped down as Labor leader after his election loss last month. The election involved separate votes of party members and party MPs, with equal weight given to each.

Mr Shorten, a 46-ear-old party power-broker, won the overall ballot despite losing the primary vote to his rival Anthony Albanese by 40 per cent to 60 per cent. However, Mr Shorten won 64 per cent of the vote in the ballot of Labor MPs.

Mr Shorten gained national attention during his role in updating the public during a mining collapse in 2006 in which two miners were trapped underground for two weeks. He is an effective communicator but has been tarnished by his role in supporting Julia Gillard to topple Mr Rudd in 2010 and then supporting Mr Rudd to oust Ms Gillard in June.

Mr Shorten said the party’s debilitating disunity was “in the past”.

“There is no doubt that Labor’s been through some difficult times while it was in Government,” he said.

“But what people have with me is someone who will always try and work out what is the best interests of the nation first, and then the best interests of Labor, and that’s how I approach my decisions.”